If you knew they were non-elect would you preach?

Assume for a moment that you were called to minister to a group of reprobates, and you happened to know for a fact that they would never come to eternal life, ever, no matter what you did or said, moreover they would only wax from bad to worse until they perished utterly.
Would you preach to them the gospel? Would you invite them to be saved?

Under the system of hyper and high Calvinism the answer would be a resounding "No!!!!"  because of the fact that no provision is available for them. Christ died on the cross to make a way only for the elect to come to Him; He did not die to save the goats. There is nothing to appeal to, there is no salvation available for them, no hope for them, no salvation waiting for them.

This situation actually happened. Isaiah 6:9,11 "And he said, "Go, and say to this people: "'Keep on hearing, but do not understand; keep on seeing, but do not perceive.'...Then I said, "How long, O Lord?" And he said: "Until cities lie waste without inhabitant, and houses without people, and the land is a desolate waste" Go Isaiah, and tell them to gospel. Tell them what I said and what my message is, and tell it until they die in their obstinacy.

The high Calvinist will point out that Isaiah was sent to make their ears closed and not to save them. To this I point out their misunderstanding, because in the very next book, Jeremiah, God reiterates this same message.
"They will fight against you, but they shall not prevail against you, for I am with you, declares the LORD, to deliver you." (Jeremiah 1:19).  He goes on, "For twenty-three years, from the thirteenth year of Josiah the son of Amon, king of Judah, to this day, the word of the LORD has come to me, and I have spoken persistently to you, but you have not listened. You have neither listened nor inclined your ears to hear, although the LORD persistently sent to you all his servants the prophets, saying, 'Turn now, every one of you, from his evil way and evil deeds, and dwell upon the land that the LORD has given to you and your fathers from of old and forever." (Jeremiah 25:3-5)

And just for kicks, let's go to the next prophet in, Ezekiel, where God calls him to be a watchman explicitly twice Eze 3:17, 33:7 "So you, son of man, I have made a watchman for the house of Israel. Whenever you hear a word from my mouth, you shall give them warning from me." That is, he was to preach the word so that they would be amply warned and discouraged from their sins. Yet Ezekiel was not fooled about the response to his message, as he was given foreknowledge they would expressly not listen (33:31) "And they come to you as people come, and they sit before you as my people, and they hear what you say but they will not do it; for with lustful talk in their mouths they act; their heart is set on their gain, And behold, you are to them like one who sings lustful songs with a beautiful voice and plays  well on an instrument, for they hear what you say, but they will not do it." And yet, all things considered, still his message was to be (v11) "Say to them, As I live, declares the Lord GOD, I have no pleasure in the death of the wicked, but that the wicked turn from his way and live; turn back, turn back from your evil ways, for why will you die, O house of Israel?"

I'll skip the fact that Jesus knew exactly what was in the hearts of men, and did not commit himself to men, but still preached them the gospel. Or the fact that He expressly called to Judas, empowered him to cast out demons, and join him to Himself in ministry, and yet knew that Judas would betray Him. That would just be too easy.

God has purposely hidden from us who is and isn't elect. But even if He didn't, He has expressly proven in Scriptures that He wants us to preach the gospel to all creatures under heaven. He wants His proposal of mercy indiscriminately offered to all so that everyone would know How gracious He is.
This is the reason we are to lend to those who cannot give back, and be kind to those who will not show us kindness in return, because in so doing, and in so being, we demonstrate the character of God. The God who has made all things beautiful and causes the sun to shine, even when men refuse to open their eyes and look. He radiates mercy, beauty, and love like the sun radiates heat. He just is. And any philosophy that doesn't have us end up there needs to be re-examined.